LM-Curve formula question

An LM Curve can be described as following

$$M^d(Y,i) = M_0 + M_1Y – M_2i$$

$$M^d = M/P$$

M and P are exogen

I know that $$i$$ is interest rate, and Y is GDP.

Why is $$M_1$$ and $$M_2$$ positive? And what does $$M_0$$ represent?

I can't quite wrap my head around it

Here;

$$M^d(Y,i)$$ is the demand for money.

$$M_0$$ is the ‘autonomous’ demand for money, i.e. demand for money that would not depend on income or interest rate.

$$M_1$$ is the effect that real income/output has on demand for money. It will be positive because ceteris paribus when there is more goods and services around people demand more money for carrying out transactions.

$$M_2$$ is the effect nominal interest rate has on money demand. It is actually negative not positive, and the reason why it is negative is that if interest rate is higher people demand less money both because it is more expensive to get (borrow) money and because with higher interest rate people prefer to save more and postpone their purchases to the future so they need less money.

• That was what i originally thought, it makes sense that the nominal interest is negative but my assignment says that i need to know why both $l_1$ and $l_2$ is positive, im not sure if its a mistake in the assignment text or something – Emil B Jan 22 at 14:13
• @EmilB I don’t know the details of the assignment. The coefficient on interest rate is definitely negative. You can check that in any macro textbook for example Blanchard et al macroeconomics a European perspective (see chapters on IS-LM) maybe the assignment is referring to LM equilibrium here you actually solve for output which will look like $Y=b_0 +b_1 M/P + b_2 i$ where betas will be the coefficients you get while deriving the equilibrium and M/P is the real money balance. Regardless for any clarification on what is meant by your assignment you need to contact your teacher there is – 1muflon1 Jan 22 at 14:17
• No way how strangers on the internet can know what your teacher means in his assignment. Maybe he made a typo or he means something else. – 1muflon1 Jan 22 at 14:17
• I updated it to give more information, however im not sure it even matters. – Emil B Jan 22 at 14:22
• @EmilB no it does not matter – 1muflon1 Jan 22 at 14:23